I suspect that the X11 cut buffer is what's munging your data. You could test this by not using it...

# create a string with binary data
my $binary="string\000with\000nulls";
# empty out the entry widget
$entrywidget->delete(0,"end");
# insert the data
$entrywidget->insert(0,$binary);
# pull back the data with get and compare to the
# original data
my $gotback=$entrywidget->get();

if ($binary ne $gotback) {
    print "hmm...buggy?\n";
    # throw in some hexdumps here ?
}
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If you can't solve the problem with binary data, perhaps you could have the user input the binary data with some sort of encoding (Base64, urlencoded,etc) ?